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A uniform momentum zone-vortical fissure model of the turbulent boundary layer. (English) Zbl 1415.76329
Summary: Recent studies reveal that at large friction Reynolds number $$\delta^+$$ the inertially dominated region of the turbulent boundary layer is composed of large-scale zones of nearly uniform momentum segregated by narrow fissures of concentrated vorticity. Experiments show that, when scaled by the boundary-layer thickness, the fissure thickness is $$O(1/\sqrt{\delta^+})$$, while the dimensional jump in streamwise velocity across each fissure scales in proportion to the friction velocity $$u_\tau$$. A simple model that exploits these essential elements of the turbulent boundary-layer structure at large $$\delta^+$$ is developed. First, a master wall-normal profile of streamwise velocity is constructed by placing a discrete number of fissures across the boundary layer. The number of fissures and their wall-normal locations follow scalings informed by analysis of the mean momentum equation. The fissures are then randomly displaced in the wall-normal direction, exchanging momentum as they move, to create an instantaneous velocity profile. This process is repeated to generate ensembles of streamwise velocity profiles from which statistical moments are computed. The modelled statistical profiles are shown to agree remarkably well with those acquired from direct numerical simulations of turbulent channel flow at large $$\delta^+$$. In particular, the model robustly reproduces the empirically observed sub-Gaussian behaviour for the skewness and kurtosis profiles over a large range of input parameters.

##### MSC:
 76F40 Turbulent boundary layers
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##### References:
 [1] Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 19, 4, (2007) · Zbl 1146.76307 [2] Adrian, R. J.; Meinhart, C. D.; Tomkins, C. D., Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech., 422, 1-54, (2000) · Zbl 0959.76503 [3] Chauhan, K.; Philip, J.; Desilva, C. M.; Hutchins, N.; Marusic, I., The turbulent/nonturbulent interface and entrainment in a boundary layer, J. Fluid Mech., 742, 119-151, (2014) [4] Chauhan, K.; Philip, J.; Marusic, I., Scaling of the turbulent/non-turbulent interface in boundary layers, J. Fluid Mech., 751, 298-328, (2014) [5] Chen, C.-H. P.; Blackwelder, R. F., Large-scale motion in a turbulent boundary layer: a study using temperature contamination, J. Fluid Mech., 89, 1-31, (1978) · Zbl 0397.76051 [6] Chini, G. P.; Montemuro, B.; White, C. M.; Klewicki, J. C., A self-sustaining process model of inertial layer dynamics in high Reynolds number turbulent wall flows, Phil. Trans. R. Soc. Lond. A, 375, (2017) [7] Corrsin, S.; Kistler, A. L. [8] Eisma, J.; Westerweel, J.; Ooms, G.; Elsinga, G. E., Interfaces and internal layers in a turbulent boundary layer, Phys. Fluids, 27, 5, 55103, (2015) [9] Eyink, G. L., Turbulent flow in pipes and channels as cross-stream ‘inverse cascades’ of vorticity, Phys. Fluids, 20, (2008) · Zbl 1182.76237 [10] Ishihara, T.; Kaneda, Y.; Hunt, J. C. R., Thin shear layers in high Reynolds number turbulence - DNS results, Flow Turbul. Combust., 91, 895-929, (2003) [11] Jimenez, J.; Pinelli, A., The autonomous cycle of near-wall turbulence, J. Fluid Mech., 389, 335-339, (1999) · Zbl 0948.76025 [12] Johansson, A. V.; Alfredsson, P. H., Evolution and dynamics of shear-layer structures in near-wall turbulence, J. Fluid Mech., 224, 579-599, (1991) · Zbl 0717.76057 [13] Klewicki, J., Reynolds number dependence, scaling and dynamics of turbulent boundary layers, J. Fluids Engng, 132, (2010) [14] Klewicki, J. C., On the singular nature of turbulent boundary layers, Procedia IUTAM, 9, 69-78, (2013) [15] Klewicki, J. C.; Falco, R. E., Spanwise vorticity structure in turbulent boundary layers, Intl J. Heat Fluid Flow, 17, 363-376, (1996) [16] Klewicki, J. C.; Falco, R. E.; Foss, J. F., Some characteristics of the vortical motions in the outer region of turbulent boundary layers, J. Fluids Engng, 114, 530-536, (1992) [17] Klewicki, J.; Fife, P.; Wei, T., On the logarithmic mean profile, J. Fluid Mech., 638, 73-93, (2009) · Zbl 1183.76766 [18] Klewicki, J.; Fife, P.; Wei, T.; Mcmurtry, P., A physical model of the turbulent boundary layer consonant with mean momentum balance structure, Phil. Trans. R. Soc. Lond. A, 365, 1852, 823-839, (2007) · Zbl 1152.76407 [19] Klewicki, J. C.; Hirschi, C. R., Flow field properties local to near-wall shear layers in a low Reynolds number turbulent boundary layer, Phys. Fluids, 16, 4163, (2004) · Zbl 1187.76275 [20] Klewicki, J. C.; Metzger, M. M.; Kelner, E.; Thurlow, E., Viscous sublayer flow visualizations at R_{𝜃}≃ 1 500 000, Phys. Fluids, 7, 857, (1995) [21] Klewicki, J.; Oberlack, M., Finite Reynolds number properties of a turbulent channel flow similarity solution, Phys. Fluids, 27, 9, (2015) [22] Klewicki, J.; Philip, J.; Marusic, I.; Chauhan, K.; Morrill-Winter, C., Self-similarity in the inertial region of wall turbulence, Phys. Rev. E, 90, (2014) [23] Klewicki, J. C., A description of turbulent wall-flow vorticity consistent with mean dynamics, J. Fluid Mech., 737, 176-204, (2013) · Zbl 1294.76179 [24] Klewicki, J. C., Self-similar mean dynamics in turbulent wall flows, J. Fluid Mech., 718, 596-621, (2013) · Zbl 1284.76205 [25] Klewicki, J. C.; Hill, R. B., Spatial structure of negative ∂u/∂y in a low R_{𝜃} turbulent boundary layer, J. Fluids Engng, 120, 4, 772-777, (1998) [26] Kwon, Y. S.; Philip, J.; Desilva, C. M.; Hutchins, N.; Monty, J. P., The quiescent core of turbulent channel flow, J. Fluid Mech., 751, 228-254, (2014) [27] Lee, M.; Moser, R. D., Direct numerical simulation of turbulent channel flow up to Re_{𝜏}≈ 5200, J. Fluid Mech., 774, 395-415, (2015) [28] Li, Y.; Perlman, E.; Wan, M.; Yang, Y.; Meneveau, C.; Burns, R.; Chen, S.; Szalay, A.; Eyink, G., A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbul., 9, (2008) · Zbl 1273.76210 [29] Marusic, I.; Adrian, R. J., The eddies and scales of wall turbulence, Ten Chapters in Turbulence, (2010), Cambridge University Press [30] Marusic, I.; Monty, J. P.; Hultmark, M.; Smits, A. J., On the logarithmic region in wall turbulence, J. Fluid Mech., 716, (2013) · Zbl 1284.76206 [31] Mathis, R.; Hutchins, N.; Marusic, I., Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers, J. Fluid Mech., 628, 311-337, (2009) · Zbl 1181.76008 [32] Meinhart, C. D.; Adrian, R. J., On the existence of uniform momentum zones in a turbulent boundary layer, Phys. Fluids, 7, 4, 694-696, (1995) [33] Morrill-Winter, C.; Klewicki, J., Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia, Phys. Fluids, 25, (2013) [34] Morrill-Winter, C. T.; Philip, J.; Klewicki, J. C., An invariant representation of mean inertia: theoretical basis for a log law in turbulent boundary layers, J. Fluid Mech., 813, 594-617, (2017) · Zbl 1383.76240 [35] Morris, S.; Stolpa, S.; Slaboch, P.; Klewicki, J., Near-surface particle image velocimetry measurements in a transitionally rough-wall atmospheric boundary layer, J. Fluid Mech., 580, 319-338, (2007) · Zbl 1113.76006 [36] Perlman, E.; Burns, R.; Li, Y.; Meneveau, C., Data exploration of turbulence simulations using a database cluster, Proc. 2007 ACM/IEEE Conf. Supercomputing, 23, (2007), Association for Computing Machinery [37] Perry, A. E.; Chong, M. S., On the mechanism of wall turbulence, J. Fluid Mech., 119, 173-217, (1982) · Zbl 0517.76057 [38] Perry, A. E.; Marusic, I., A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis, J. Fluid Mech., 298, 361-388, (1995) · Zbl 0849.76030 [39] Priyadarshana, P. J. A.; Klewicki, J. C.; Treat, S.; Foss, J. F., Statistical structure of turbulent-boundary-layer velocity-vorticity products at high and low Reynolds numbers, J. Fluid Mech., 570, 307-346, (2007) · Zbl 1106.76317 [40] Da Silva, C. B.; Hunt, J. C. R.; Eames, I.; Westerweel, J., Interfacial layers between regions of different turbulence intensity, Annu. Rev. Fluid Mech., 46, 567-590, (2014) · Zbl 1297.76074 [41] De Silva, C. M.; Hutchins, N.; Marusic, I., Uniform momentum zones in turbulent boundary layers, J. Fluid Mech., 786, 309-331, (2016) · Zbl 1381.76106 [42] De Silva, C. M.; Philip, J.; Hutchins, N.; Marusic, I., Interfaces of uniform momentum zones in turbulent boundary layers, J. Fluid Mech., 820, 451-478, (2017) · Zbl 1383.76257 [43] Sreenivasan, K. R.; Bershadskii, A., Finite-Reynolds-number effects in turbulence using logarithmic expansions., J. Fluid Mech., 554, 477-498, (2006) · Zbl 1091.76024 [44] Taylor, G. I., The transport of vorticity and heat through fluids in turbulent motion, Proc. R. Soc. Lond. A, 135, 685-702, (1932) · JFM 58.1309.03 [45] Townsend, A. A., The Structure of Turbulent Shear Flow, (1976), Cambridge University Press · Zbl 0325.76063 [46] Wei, T.; Fife, P.; Klewicki, J.; Mcmurtry, P., Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows, J. Fluid Mech., 522, 303-327, (2005) · Zbl 1065.76106 [47] Westerweel, J.; Fukushima, C.; Pedersen, J. M.; Hunt, J. C. R., Momentum and scalar transport at the turbulent-nonturbulent interface of a jet, J. Fluid Mech., 631, 199-230, (2009) · Zbl 1181.76015
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